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This higher-GCSE topic introduces differentiation of simple polynomials to find the gradient function, the gradient at a point, and the turning points of a curve. It's examined right across GCSE and iGCSE Maths. Work through it free on eClassroom, with clear worked examples and instantly-marked questions that build your confidence for the exam.
How you do it
Multiply by the power, then reduce the power by one. Differentiate each term separately, and remember a constant differentiates to zero. Substituting an x value into the derivative gives the gradient of the curve at that point.
Before you start
This builds directly on indices and gradients. From here the path runs to the whole of A-Level calculus.
What you learn
Differentiation finds the gradient function of a curve. Differentiating y gives dy⁄dx, which tells you the gradient at any point. The gradient at a particular point is found by differentiating, then substituting the x-coordinate into dy⁄dx. At a turning point the curve is momentarily flat, so the gradient is 0. The course works through differentiating powers of x, gradient at a point and turning points. Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Differentiation is a Algebra topic in the GCSE syllabus, covered here at Higher tier. The course is built from 3 concept sections, 2 worked examples and 3 check points before the exam-style set. Nearby topics in the same strand are Expanding Brackets, Factorising, Functions, Gradients & Rates of Change and Inequalities. You can drill this strand further on the Algebra revision engine, with your accuracy saved to your skill tree.
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